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Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Not pfaffian"

James Freitag has shown that the j-function is not Pfaffian using the model theory of differentially closed fields. We will work though his paper, entitled "Not pfaffian".

MC 5417

Erik Seguin, Department of Pure Mathematics, University of Waterloo

"Amenability and stability for discrete groups"

Francisco Villacis, Department of Pure Mathematics, University of Waterloo

"Integrable systems on smooth projective toric varieties"

Let X be a smooth projective toric variety of complex dimension n. We can endow X with a symplectic form coming from the Fubini-Study form on projective space. We will show that we have an action of a real n-torus on X which is Hamiltonian and gives rise to an integrable system on X.

This seminar will be held both online and in person:

Changho Han, Department of Pure Mathematics, University of Waterloo

"Brief Introduction to General MMP"

Before we dive into the less ventured area of horospherical MMP, it would be nice to first understand how the general MMP works in order to prove MMP results in horospherical settings. In that regard, I will present some motivations behind the definition of MMP singularities, and give a general overview of the general MMP.

This seminar will be held jointly online and in person:

Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets - Part III"

An effectively closed set (or $\Pi^0_1$ class) in Baire space $\omega^\omega$ is the set $[T]$ of infinite branches through a computable tree $T$. This semester in the computability seminar, we will be studying $\Pi^0_1$ classes from Cenzer \& Remmel's textbook. This week, we will conclude chapter 2 by discussing some applications of $\Pi^0_1$ classes in computability theory.

MC 5403

Hanming Liu, Department of Pure Mathematics, University of Waterloo

"Heegaard Floer Homology"

This will be an introduction to Heegaard Floer homology. We will aim to present its definition and state some topological applications.

MC 5403

Debanjana Kundu, University of Toronto

"Heuristics for  anti-cyclotomic $\mathbb{Z}_p$-extensions"

For an imaginary quadratic field, there are two natural $\mathbb{Z}_p$-extensions, the cyclotomic and the anticyclotomic. We'll start with a brief description of Iwasawa theory for the cyclotomic extensions, and then describe some computations for anticyclotomic  $\mathbb{Z}_p$ extensions, especially the fields and their class numbers. This is joint work with LC Washington.

This seminar will be held both online and in person

Gianluca Basso, Université Lyon 1

"Kaleidoscopic groups and the generic point property"

Xuemiao Chen, Department of Pure Mathematics, University of Waterloo

"Bogomolov inequality"

After introducing some necessary basics, we will present Miyaoka's elegant proof of the Bogomolov inequality for slope semistable bundles over projective smooth surfaces.

MC 5403

Sourabhashis Das, Department of Pure Mathematics, University of Waterloo

"Chapter 2 – Algebraic curves"

In this first talk of the learning seminar, we will introduce algebraic curves and present basic facts about these curves which are essential in the study of elliptic curves. In particular, we will talk about the divisor group associated to such curves and discuss certain important results such as the Riemann-Roch theorem.

This seminar will be held both online and in person: